This is how to get the "evolved" bakugan in the game, after story is complete.

Unlockable	How to unlock
Battle Axe Vladitor	Beat Marduk without giving up and cards.
Blade Tigrerra	Beat Runo in a battle royal.
Delta Dragonoid II	Beat Dan in a battle royal.
Dual Hydranoid	Beat Masquerade in a battle royal.
Hammer Gorem	Beat Julie in a battle royal.
Omega Leonidus	Get before doing the last battle in story mode.
Preyas II	Beat Marucho in a battle royal.
Storm Skyress	Beat Shun in a battle royal.